Theorems · Theorem · linear algebra

Submodule.dualCoannihilator_map_linearEquiv_flip

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] (e : N ≃ₗ[R] Module.Dual R M) (p : Submodule R M),
  (Submodule.map (↑e).flip p).dualCoannihilator = Submodule.map (↑e.symm) p.dualAnnihilator

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Basic

Cited by

2 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule